- #1
sphlanx
- 11
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Homework Statement
Hello again. First of all thanks to anyone who has replied to my previous questions.
Now, the question that troubles me is:
We are given a matrix A2x2 with some random values and we are asked to say if there is a linear map which has A as its map for the standar basis.
A= 2 1
-5 8
Homework Equations
The Attempt at a Solution
If A is the matrix of some linear map for the standar basis that means that:
f(1,0)=2(1,0) -5(0,1)
f(0,1)=1(1,0) +8(0,1)
so f(1,0)=(2,-5) and f(0,1)=(1,8)
Although the question only asks to say if such a linear map exists (it obviously does but i don't know how to prove it) I would be glad if someone could instruct me on finding formulas for linear maps when we have their matrix.